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7552890 
Journal Article 
The first Zagreb index 30 years after 
Gutman, I; Das, KC 
2004 
1 
Match (Mülheim an der Ruhr, Germany)
ISSN: 0340-6253 
50 
83-92 
WOS:000220000200007 
The graph invariant M-1, known under the name first Zagreb index, equal to the sum of the squares of the degrees of the vertices of the respective (molecular) graph, was first considered by Trinajstic and one of the present authors in 1972. We show that M-1 is related to a number of other quantities of interest in chemical graph theory, and point out some of its general mathematical properties. In particular, the trees with minimal and maximal M-1 are the path and the star, respectively. Several lower and upper bounds for M-1 are reported.